The response of a cortical neuron is a function of the activity of other neurons that provide synaptic input to it. Theoretical models allow such function to be nonlinear, but the combination of input activities that it acts upon is typically considered linear. This results in all inputs having the same qualitative effect on the output. However, experiments reveal that neuronal behavior often deviates notoriously from this picture. One example is the interaction between retinal and eye-position signals in posterior parietal neurons, where the extra-retinal information modulates the amplitude of responses triggered by visual stimuli. This is often described as a multiplicative interaction between two terms, one that drives the neuron and another that regulates its gain. The distinction between classical and extra-classical receptive fields is another example of direct versus modulatory influences. Circuits of gain-modulated units are known to be ideally suited for performing certain kinds of computations, but their dynamics are virtually unknown. By combining theoretical models and computer simulations, we will explore the idea that multiplicative interactions between neurons give rise to neural circuits with dynamical properties that are richer, more powerful, and closer to reality than those of traditional models. A variety of new network models will be constructed in which inputs are segregated into two classes: ones that drive the target neuron and others that modulate the amplitude of the driven response. Initial models will be based on mean firing rate descriptions, and will be compared to traditional models without explicit gain interactions. Circuits with stereotyped connectivities (uniform, random, center-surround) will be studied first. Preliminary results reveal extremely interesting and robust dynamics in these models: they may amplify weak inputs but avoid runaway behavior; they may be set at two distinct response levels, acting as a switch; they may naturally give rise to patterns of self-sustained activity, as in working memory; they may produce traveling waves of activity. These behaviors will be catalogued. Circuits of spiking neurons exhibiting similar dynamics will also be developed. This will require investigating the biophysical mechanisms underlying gain modulation. All along, gain-modulated spiking networks will be used to construct detailed models of sensory and motor systems that have been well characterized experimentally.